Gen Abdel Fattah al-Sissi, who is also the country's Defence Minister, made the comments two days after President Muhammed Mursi declared a month-long emergency in riot-hit Port Said, Ismailia and Suez provinces and deployed military in the region along the strategic Suez Canal.
In comments posted on his Facebook page, Gen al-Sissi said such a collapse could "threaten future generations".
Overnight, thousands of people in the worst violence hit cities ignored the curfew and temporary state of emergency to take to the streets.
According to state TV, a total of 590 people were injured in violence across the country yesterday alone, with most of them in Port Said.
Medics said two people were killed in clashes in Port Said late last night while another was shot dead near Tahrir Square here.
Gen Sissi's statement appears to be a "veiled threat to protesters and opposition forces as well as an appeal for calm and an attempt to reassure Egyptians about the role of the military", BBC reported.
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"The continuing conflict between political forces and their differences concerning the management of the country could lead to a collapse of the state and threaten future generations," Sissi said.
He said the economic, political and social challenges facing Egypt represented "a real threat to the security of Egypt and the cohesiveness of the Egyptian state".
He described the army as "the solid and cohesive block" on which the state rests. (MORE)